Quantum mechanics and light behaviors in daily life

2 min read

Light travels in a straight line. When light is reflected by a mirror, the incoming angle is equal to the reflection angle. When light enters water, it changes its directions according to Snell’s law. …

Or does it?

These light behaviors are not as intuitive as we think if we really want to explain them in quantum mechanics. We have to keep in mind, when a light particle – photon – travels from point A to point B, the photon takes all paths available in the universe! Correct, not just the straight line between A and B, but also any weird curves you can imagine starting from A to B.

“Photon Dance 8” by zwopper, Deviant Art

First, let’s show that photons actually travel in non-classical paths. In the setting below, light is emitted from the left and received by the small “black hole” on the right. There is a wall between them so the light can’t travel in the straight line. A mirror is placed at the bottom. You might think, the only way for the light to reach the “black hole” is to travel in the classical path shown below.

Light is reflected at the center of the mirror

Now, if one removes the central and right part of the mirror, and also removes some parts on the left, as shown in the figure below, you would think that there is no light reaching the black hole. After all, the central part of the mirrow is where the light get reflected and reach the black hole.

Light also takes other paths

Contrary to what we believe, some light does reach the “black hole”! This demonstrates that the photons take all paths!

(The examples/figures above are from video by The Science Asylum. Another equally interesting video from the same channel is https://www.youtube.com/watch?v=cep6eECGtw4 )

The Science Asylum’s Youtube video

Next, a natural question is, why we see the light travels in straight line? Why it is reflected by the mirror with equal incoming and reflecting angle?

We will have to understand that a photon has “phases”. The term “phase” is familiar to us when we study “waves”. In a nutshell, if two waves have aligned phases, when they come together they will form a bigger wave; if the phases are not aligned, then the final wave will be smaller or even disappears!

Aligned and anti-aligned phases

It turns out while the photons do take all the paths, only the “classical” paths are where the photons have aligned phases! To work this out, we really need to do some calculations. Here are the steps copied from https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Quantum_Behaviour

  1. Define the light source.
  2. Work out the frequency of the photon.
  3. Define any objects which the light cannot pass through.
  4. Define the first point you wish to consider.
  5. Define a set of paths from the source to the point being considered, the more, the better.
  6. Work out the time taken to traverse one of the paths.
  7. Work out how many phasor rotations this corresponds to.
  8. Draw an arrow representing the final phasor arrow.
  9. Repeat steps 6-8 for each of the paths.
  10. Add all the phasor arrows together, tip-to-tail.
  11. Square the amplitude of this resultant phasor arrow to gain the intensity of the light at this point. It may help to imagine a square rotating around, instead of an arrow.
  12. Repeat steps 4-11 for every point you wish to consider. The more points you consider, the more accurate your probability distribution will be.
  13. Compare all the resultant intensities to gain a probability distribution which describes the probabilities of a photon arriving at one point to another. For example, if the intensity of light at one point is two times the intensity of light at another, then it is twice as likely that a photon will arrive at the first point than the second.
  14. If all the points being considered were on a screen, the intensities show you the relative brightnesses of light at each of the points.

I admit it’s not very easy calculations. But what matters is that we understand photons do take all the paths available, and when there are no photons, it’s only because the phases of the photons are misaligned.

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该文章可以通过该链接完整阅读(包括图片。这些图片有时微信禁止转载)。 我们印象当中,发文章需要做大量的实验和分析。实验对象可以是原子、病毒,可以是疾病、人群,也可以是恒星、宇宙。可是,如果分析的对象是文献本身,这样的研究有吗?能发文章吗? 小编虽然在科研领域20年,但是对这个问题还没有明确答案。于是这两天埋头钻研,结果脑洞大开,发现了一个原来从没听说过的领域:文献计量学,英文叫 Bibliometrics。借用百度百科的话,文献计量学是指用数学和统计学的方法,定量地分析一切知识载体的交叉科学。而这个领域竟然已存在100余年,不得不承认自己实在是孤陋寡闻。 于是,我们用“文献分析”的方法分析了“文献分析”类的文献(咦,怎么有点拗口?),看看有哪些意想不到的发现。我们用的关键词非常简单,就是 bibliometrics。数据来源是PubMed,分析工具是文献鸟的大分析。 01 — 上万篇论文用了“文献计量学” 首先,不仅有论文用了文献计量学的方法,而且有很多。在PubMed数据库里有一万余篇这类的论文。如果看趋势,我们发现在2005-2010增长速度较快,这几年稳定到每年750余篇。 02 — “文献计量学”论文可以发表在好期刊 那么,这上万篇的论文都发表在什么期刊?是灌水期刊吗?从上图的分布图来看,文献计量学的论文在各类期刊都有。在前25个期刊中,有Nature(254篇)、Science(74篇)、Lancet(41篇)、JAMA(32篇)这类顶尖文章(黄色标记),也有J Clin Epidemiol等这样的不错的期刊(绿色),当然也有影响力更低的期刊。 这么多Nature、Science等文章,自然引起了小编的怀疑和警惕。难道我通过分析文献就可以发表CNS文章?是不是太简单了?于是,小编点击进去,看看有哪些文章发表在这些顶级期刊。 果真不出所料,绝大部分在顶尖期刊的论文是评论、新闻、通信类型的。但是,通过仔细排查,我们还是找到了正规的、研究类的文章。下面举几个例子。 Lancet. 2019 Feb 9;393(10171):550-559. doi: 10.1016/S0140-6736(18)32995-7....
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